To. CompuChip:
Thank you for letting me know. I tried to split the part that I don't know from the original problem and made a mistake during this procedure. BTW, it seems Office_Shredder knows the original one.
To. Office_Shredder:
Yes. The problem is from "the mgf of Chi_sq(n) becomes...
Application on the limit definition of "e"
Hi, I have known that:
(i) (1+\frac{a}{n})^n=((1+\frac{a}{n})^\frac{n}{a})^a\to e^a
(ii) (1-\frac{1}{n})^n=(\frac{n-1}{n})^n=(\frac{1}{\frac{n}{n-1}})^{(n-1)+1}=(\frac{1}{1+\frac{1}{n-1}})^{(n-1)}\cdot (\frac{1}{1+\frac{1}{n-1}}) \to \frac{1}{e}\cdot...